Estimating Matching Affinity Matrices under Low-Rank Constraints

Arnaud Dupuy, Alfred Galichon () and Yifei Sun
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Arnaud Dupuy: uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg
Alfred Galichon: NYU - NYU System, CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique
Yifei Sun: CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System

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Abstract: In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high-dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization that effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors that are relevant for matching.

Date: 2019-12
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Published in Information and Inference, 2019, 8 (4), pp.677-689. ⟨10.1093/imaiai/iaz015⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:spmain:hal-03948102

DOI: 10.1093/imaiai/iaz015

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